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Mat. Zametki, 1969, Volume 6, Issue 4, Pages 381–392 (Mi mz6944)  

On group rings of abelian $p$-groups of any cardinality

S. D. Bermana, T. Zh. Mollovb

a Kharkov State University
b Plovdiv High Pedagogical Institute (Bulgaria)

Abstract: The problem is studied of the connection between an Abelian $p$-group $G$ of arbitrary cardinality and its group ring $LG$, where $L$ is a ring with unity nonzero characteristic $n\equiv0(\mod p)$, with $p$ being a prime. In particular, it is shown that group ring $LG$ defines to within isomorphism the basis subgroup of group $G$. If reduced Abelian $p$-group $G$ has finite type and if its Ulm factors decompose into direct products of cyclic groups, then group ring $LG$ determines group $G$ to within isomorphism.

Full text: PDF file (992 kB)

English version:
Mathematical Notes, 1969, 6:4, 686–692

Bibliographic databases:

UDC: 512.4
Received: 17.06.1968

Citation: S. D. Berman, T. Zh. Mollov, “On group rings of abelian $p$-groups of any cardinality”, Mat. Zametki, 6:4 (1969), 381–392; Math. Notes, 6:4 (1969), 686–692

Citation in format AMSBIB
\Bibitem{BerMol69}
\by S.~D.~Berman, T.~Zh.~Mollov
\paper On group rings of abelian $p$-groups of any cardinality
\jour Mat. Zametki
\yr 1969
\vol 6
\issue 4
\pages 381--392
\mathnet{http://mi.mathnet.ru/mz6944}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=254155}
\zmath{https://zbmath.org/?q=an:0204.35201|0187.29704}
\transl
\jour Math. Notes
\yr 1969
\vol 6
\issue 4
\pages 686--692
\crossref{https://doi.org/10.1007/BF01093802}


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